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Straight Line Homotopy
Definition: Let f and g be any two maps of a space X into R^2. It is easy to see that f and g are homotopic; the map F(x, t) = (1-t)f(x) + tg(x) is a homotopy between them. It is called a straight-line homotopy because it moves the point f(x) to the point g(x) along the straight-line segment joining them.
Source: Topology (second edition) by James R. Munkres